PPT: Shapes and Patterns | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

 Page 1


Shapes and 
Patterns
Page 2


Shapes and 
Patterns
What is a Pattern?
A pattern is formed by repeating a unit, which may be a set of numbers or shapes, according to a 
rule.
For Example - Patterns in the border of dupatta, bedsheets, floors, etc.
These are called border patterns. We see that border patterns enhance the original beauty.
These border patterns are formed by repeating a certain shape or unit in one direction.
Following a basic symmetry repetition, maybe of translation, vertical reflection or horizontal 
reflection.
Page 3


Shapes and 
Patterns
What is a Pattern?
A pattern is formed by repeating a unit, which may be a set of numbers or shapes, according to a 
rule.
For Example - Patterns in the border of dupatta, bedsheets, floors, etc.
These are called border patterns. We see that border patterns enhance the original beauty.
These border patterns are formed by repeating a certain shape or unit in one direction.
Following a basic symmetry repetition, maybe of translation, vertical reflection or horizontal 
reflection.
Tiling and Tessellation
We often use tiles of the same shape or a 
combination of shapes to cover a region.
Shapes that have equal sides are called 
regular shapes.
Example -
Place 2 regular pentagons around a point 
³ a small empty space is left.
Try to fit a 3rd pentagon ³ shapes 
overlap.
So, regular pentagons alone cannot 
tessellate (they can¾t fill a floor perfectly).
Tessellation (tiling) = covering a surface without any gaps or overlaps.
Page 4


Shapes and 
Patterns
What is a Pattern?
A pattern is formed by repeating a unit, which may be a set of numbers or shapes, according to a 
rule.
For Example - Patterns in the border of dupatta, bedsheets, floors, etc.
These are called border patterns. We see that border patterns enhance the original beauty.
These border patterns are formed by repeating a certain shape or unit in one direction.
Following a basic symmetry repetition, maybe of translation, vertical reflection or horizontal 
reflection.
Tiling and Tessellation
We often use tiles of the same shape or a 
combination of shapes to cover a region.
Shapes that have equal sides are called 
regular shapes.
Example -
Place 2 regular pentagons around a point 
³ a small empty space is left.
Try to fit a 3rd pentagon ³ shapes 
overlap.
So, regular pentagons alone cannot 
tessellate (they can¾t fill a floor perfectly).
Tessellation (tiling) = covering a surface without any gaps or overlaps.
Shapes That Tessellate
Equilateral Triangles
Regular triangles when 
fitted around a point leave 
no gaps and there is no 
overlap.
Squares
Four squares fit perfectly 
around a point with no 
gaps or overlaps.
Regular Hexagons
Three hexagons fit 
perfectly around a point 
with no gaps or overlaps.
Page 5


Shapes and 
Patterns
What is a Pattern?
A pattern is formed by repeating a unit, which may be a set of numbers or shapes, according to a 
rule.
For Example - Patterns in the border of dupatta, bedsheets, floors, etc.
These are called border patterns. We see that border patterns enhance the original beauty.
These border patterns are formed by repeating a certain shape or unit in one direction.
Following a basic symmetry repetition, maybe of translation, vertical reflection or horizontal 
reflection.
Tiling and Tessellation
We often use tiles of the same shape or a 
combination of shapes to cover a region.
Shapes that have equal sides are called 
regular shapes.
Example -
Place 2 regular pentagons around a point 
³ a small empty space is left.
Try to fit a 3rd pentagon ³ shapes 
overlap.
So, regular pentagons alone cannot 
tessellate (they can¾t fill a floor perfectly).
Tessellation (tiling) = covering a surface without any gaps or overlaps.
Shapes That Tessellate
Equilateral Triangles
Regular triangles when 
fitted around a point leave 
no gaps and there is no 
overlap.
Squares
Four squares fit perfectly 
around a point with no 
gaps or overlaps.
Regular Hexagons
Three hexagons fit 
perfectly around a point 
with no gaps or overlaps.
Mixed Tessellations
Patterns can use more than one shape together.